Back in June, I posted about mathematical objects made on a lathe. Here are two more difficult examples, both by Claude Lethiecq, a wood turner working near Montreal. I have examined these in person and they are truly masterpieces of technique. This first object consists of twelve hollow spheres each free to jiggle but interlocked (via five holes linked through five holes) with a single larger sphere, plus another smaller spiked sphere floating freely in the inside. Unbelievably, everything was carved in place from a single block of wood, with no gluing (except the darker finials).

Nested spheres are made with special-purpose cutters that fit along the curve between two spheres as they turn on the lathe. When there are many holes in the outside of such a sphere, the cutter only has to reach halfway to the next hole, to remove all the intervening material. But in the example below, there is only one exterior hole. Through it, you see three nested spheres and a spiked center piece, which are free to rotate in the interior. Again, the complete construction was made on a lathe from a single block of solid wood with no gluing. Imaging how the curved cutter had to be able to reach in through the large outer hole and curve all the way around to the back to free the inner spheres. Very special curved cutters were specially made for this.